Question

In a right triangle abc right angle at c if tana=1 than verify that 2sina×cosa=1

Answer 1

TanA=1=Tan45°

A=45°.C=90°B=90-45=45°

hence its verified

Answer 2

⇒ Given :- ABC is a right angled triangle at C

tan A = 1

⇒ To verify :- 2 sin A cos A = 1.

⇒ Solution:- In ∆ ABC

tan A = 1

BC/AC = 1

BC = x & AC = x

By Pythagoras theorem

AB^2 = AC^2 + BC^2

AB^2 = x^2 + x^2

AB = √2x

sin A = BC/AB

= x/√2x

= 1/√2x

cos A = AC/AB

= x/√2x

= 1/√2x

2 sin A cos A =

2 × 1/√2 × 1/√2

= 1

Hence verified!